The resultant of two vector of equal magnitude is twice of magnitude of either of the vectors the angle between them is

If ${\rm{\vec A}}{\rm{.\vec B}} = AB,$, then the angle between ${\rm{\vec A}}\,{\rm{and}}\,{\rm{\vec B}}$ is

The resultant of two vector of equal magnitude is twice of magnitude of either of the vectors the angle between them is

Given ${\rm{\vec P}} = 3\hat j + 4\hat k\,and\,{\rm{\vec Q}} = 2\hat i + 5\hat k$. The magnitude of the scalar product of these vectors is

If  ${\rm{\vec P}} = 4{\rm{\hat i}} - 2{\rm{\hat j}} + 6{\rm{\hat k\;}}\,\,\,{\rm{and}}\,\,{\rm{\vec Q}} = {\rm{\hat i}} - 2{\rm{\hat j}} - 3{\rm{\hat k}}$ , then the angle which ${\rm{\vec P}} + {\rm{\vec Q}}$ makes with x-axis is

The resultant of two vector of equal magnitude is twice of magnitude of either of the vectors the angle between them is

The vector projection of a vector $3\widehat i + 4\widehat k$ on y-axis is

If ${{\rm{\vec A}}_1}\,and\,{{\rm{\vec A}}_2}$ are two non-collinear unit vectors and if $\left| {{{{\rm{\vec A}}}_1} + {{{\rm{\vec A}}}_2}} \right| = \sqrt 3$, then the value of $\left( {{{{\rm{\vec A}}}_1} - {{{\rm{\vec A}}}_2}} \right).\left( {2{{{\rm{\vec A}}}_1} + {{{\rm{\vec A}}}_2}} \right)$

A vector $\overrightarrow A$ points vertically upward and $\overrightarrow B$ points towards north. The vector product of $\overrightarrow A \, imes \,\overrightarrow B$ is

The component of $\overrightarrow A$ along $\overrightarrow B$ is 2 times that of the component of $\overrightarrow B$ along $\overrightarrow A$. Then A : B is

If $\overrightarrow A = 2\hat i + 3\hat j + 4\hat k\,\,and\,\,{\rm{\vec B}} = 4\hat i + 3\hat j + 2\hat k$, then angle between $\overrightarrow A$ and ${\rm{\vec B}}$ is